A four-component Camassa–Holm type hierarchy

Li, Nianhua; Liu, Q. P.; Popowicz, Ziemowit

doi:10.1016/j.geomphys.2014.05.026

Cited by 37 publications

(29 citation statements)

References 22 publications

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“…(2) the Hunter-Saxton equation [3,24] m t + m x u + 2mu x = 0, m = u xx , (1.4) (3) multicomponent generalizations of CH [8,18,19,27], for example the Geng-Xue (two-component) equation:…”

Section: Introductionmentioning

confidence: 99%

Multipeakons of a two-component modified Camassa–Holm equation and the relation with the finite Kac–van Moerbeke lattice

Chang

Szmigielski

2016

Advances in Mathematics

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A spectral and the inverse spectral problem are studied for the two-component modified Camassa-Holm type for measures associated to interlacing peaks. It is shown that the spectral problem is equivalent to an inhomogenous string problem with Dirichlet/Neumann boundary conditions. The inverse problem is solved by Stieltjes's continued fraction expansion, leading to an explicit construction of peakon solutions. Sufficient conditions for global existence of solutions are given. The large time asymptotics reveals that, asymptotically, peakons pair up to form bound states moving with constant speeds. The peakon flow is shown to project to one of the isospectral flows of the finite Kac-van Moerbeke lattice. XIANG-KE CHANG, XING-BIAO HU, AND JACEK SZMIGIELSKI Appendix A. Lax pair for peakon ODEs 24 References 26

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“…(2) the Hunter-Saxton equation [3,24] m t + m x u + 2mu x = 0, m = u xx , (1.4) (3) multicomponent generalizations of CH [8,18,19,27], for example the Geng-Xue (two-component) equation:…”

Section: Introductionmentioning

confidence: 99%

Multipeakons of a two-component modified Camassa–Holm equation and the relation with the finite Kac–van Moerbeke lattice

Chang

Szmigielski

2016

Advances in Mathematics

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“…The first (4CH) system include as a special case the (3CH) system considered by Xia, Zhou and Qiao while the second contains the two-component generalizations of Novikov system considered by Geng and Xiu. Our Lax pair is a matrix generalization of the Lax pair for the four component Camassa-Holm type hierarchy considered in [32]. Our matrix Lax representation produces a huge number of different cubic CH type equations and it will be interesting to investigate these further, especially to study the existence of infinitely many conservation laws.…”

Section: Resultsmentioning

confidence: 99%

A four component cubic peakon (4CH) equation

Popowicz¹

2017

J. Phys. A: Math. Theor.

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“…As pointed out in Ref. [19], the three-component system (5) is the compatible condition of the spectral problem (4) and associated auxiliary problem…”

Section: A Reciprocal Transformationmentioning

confidence: 98%